fcn_Dh_Dq.m

function Dh_Dq = fcn_Dh_Dq(s,alpha,deltheta)
s1=s; s2=s; s3=s; s4=s;
Dh_Dq(1,1)=-(6*alpha(1,6)*s1^5 - 6*alpha(1,7)*s1^5 - 6*alpha(1,1)*(s1 - 1)^5 + 6*alpha(1,2)*...
         (s1 - 1)^5 + 30*alpha(1,2)*s1*(s1 - 1)^4 - 30*alpha(1,3)*s1*(s1 - 1)^4 + 30*alpha(1,6)*s1^4*(s1 - 1) - 15*...
         alpha(1,5)*s1^4*(2*s1 - 2) - 60*alpha(1,3)*s1^2*(s1 - 1)^3 + 60*alpha(1,4)*s1^2*(s1 - 1)^3 + 60*alpha(1,4)*...
         s1^3*(s1 - 1)^2 - 60*alpha(1,5)*s1^3*(s1 - 1)^2)/deltheta;
  Dh_Dq(1,2)=1 - (6*alpha(1,6)*s1^5 - 6*alpha(1,7)*s1^5 - 6*alpha(1,1)*(s1 - 1)^5 + 6*alpha(1,2)*...
         (s1 - 1)^5 + 30*alpha(1,2)*s1*(s1 - 1)^4 - 30*alpha(1,3)*s1*(s1 - 1)^4 + 30*alpha(1,6)*s1^4*(s1 - 1) - 15*...
         alpha(1,5)*s1^4*(2*s1 - 2) - 60*alpha(1,3)*s1^2*(s1 - 1)^3 + 60*alpha(1,4)*s1^2*(s1 - 1)^3 + 60*alpha(1,4)*...
         s1^3*(s1 - 1)^2 - 60*alpha(1,5)*s1^3*(s1 - 1)^2)/deltheta;
  Dh_Dq(1,3)=0;
  Dh_Dq(1,4)=-(6*alpha(1,6)*s1^5 - 6*alpha(1,7)*s1^5 - 6*alpha(1,1)*(s1 - 1)^5 + 6*alpha(1,2)*...
         (s1 - 1)^5 + 30*alpha(1,2)*s1*(s1 - 1)^4 - 30*alpha(1,3)*s1*(s1 - 1)^4 + 30*alpha(1,6)*s1^4*(s1 - 1) - 15*...
         alpha(1,5)*s1^4*(2*s1 - 2) - 60*alpha(1,3)*s1^2*(s1 - 1)^3 + 60*alpha(1,4)*s1^2*(s1 - 1)^3 + 60*alpha(1,4)*...
         s1^3*(s1 - 1)^2 - 60*alpha(1,5)*s1^3*(s1 - 1)^2)/(2*deltheta);
  Dh_Dq(1,5)=0;
  Dh_Dq(2,1)=-(6*alpha(2,6)*s2^5 - 6*alpha(2,7)*s2^5 - 6*alpha(2,1)*(s2 - 1)^5 + 6*alpha(2,2)*...
         (s2 - 1)^5 + 30*alpha(2,2)*s2*(s2 - 1)^4 - 30*alpha(2,3)*s2*(s2 - 1)^4 + 30*alpha(2,6)*s2^4*(s2 - 1) - 15*...
         alpha(2,5)*s2^4*(2*s2 - 2) - 60*alpha(2,3)*s2^2*(s2 - 1)^3 + 60*alpha(2,4)*s2^2*(s2 - 1)^3 + 60*alpha(2,4)*...
         s2^3*(s2 - 1)^2 - 60*alpha(2,5)*s2^3*(s2 - 1)^2)/deltheta;
  Dh_Dq(2,2)=-(6*alpha(2,6)*s2^5 - 6*alpha(2,7)*s2^5 - 6*alpha(2,1)*(s2 - 1)^5 + 6*alpha(2,2)*...
         (s2 - 1)^5 + 30*alpha(2,2)*s2*(s2 - 1)^4 - 30*alpha(2,3)*s2*(s2 - 1)^4 + 30*alpha(2,6)*s2^4*(s2 - 1) - 15*...
         alpha(2,5)*s2^4*(2*s2 - 2) - 60*alpha(2,3)*s2^2*(s2 - 1)^3 + 60*alpha(2,4)*s2^2*(s2 - 1)^3 + 60*alpha(2,4)*...
         s2^3*(s2 - 1)^2 - 60*alpha(2,5)*s2^3*(s2 - 1)^2)/deltheta;
  Dh_Dq(2,3)=1;
  Dh_Dq(2,4)=-(6*alpha(2,6)*s2^5 - 6*alpha(2,7)*s2^5 - 6*alpha(2,1)*(s2 - 1)^5 + 6*alpha(2,2)*...
         (s2 - 1)^5 + 30*alpha(2,2)*s2*(s2 - 1)^4 - 30*alpha(2,3)*s2*(s2 - 1)^4 + 30*alpha(2,6)*s2^4*(s2 - 1) - 15*...
         alpha(2,5)*s2^4*(2*s2 - 2) - 60*alpha(2,3)*s2^2*(s2 - 1)^3 + 60*alpha(2,4)*s2^2*(s2 - 1)^3 + 60*alpha(2,4)*...
         s2^3*(s2 - 1)^2 - 60*alpha(2,5)*s2^3*(s2 - 1)^2)/(2*deltheta);
  Dh_Dq(2,5)=0;
  Dh_Dq(3,1)=-(6*alpha(3,6)*s3^5 - 6*alpha(3,7)*s3^5 - 6*alpha(3,1)*(s3 - 1)^5 + 6*alpha(3,2)*...
         (s3 - 1)^5 + 30*alpha(3,2)*s3*(s3 - 1)^4 - 30*alpha(3,3)*s3*(s3 - 1)^4 + 30*alpha(3,6)*s3^4*(s3 - 1) - 15*...
         alpha(3,5)*s3^4*(2*s3 - 2) - 60*alpha(3,3)*s3^2*(s3 - 1)^3 + 60*alpha(3,4)*s3^2*(s3 - 1)^3 + 60*alpha(3,4)*...
         s3^3*(s3 - 1)^2 - 60*alpha(3,5)*s3^3*(s3 - 1)^2)/deltheta;
  Dh_Dq(3,2)=-(6*alpha(3,6)*s3^5 - 6*alpha(3,7)*s3^5 - 6*alpha(3,1)*(s3 - 1)^5 + 6*alpha(3,2)*...
         (s3 - 1)^5 + 30*alpha(3,2)*s3*(s3 - 1)^4 - 30*alpha(3,3)*s3*(s3 - 1)^4 + 30*alpha(3,6)*s3^4*(s3 - 1) - 15*...
         alpha(3,5)*s3^4*(2*s3 - 2) - 60*alpha(3,3)*s3^2*(s3 - 1)^3 + 60*alpha(3,4)*s3^2*(s3 - 1)^3 + 60*alpha(3,4)*...
         s3^3*(s3 - 1)^2 - 60*alpha(3,5)*s3^3*(s3 - 1)^2)/deltheta;
  Dh_Dq(3,3)=0;
  Dh_Dq(3,4)=1 - (6*alpha(3,6)*s3^5 - 6*alpha(3,7)*s3^5 - 6*alpha(3,1)*(s3 - 1)^5 + 6*alpha(3,2)*...
         (s3 - 1)^5 + 30*alpha(3,2)*s3*(s3 - 1)^4 - 30*alpha(3,3)*s3*(s3 - 1)^4 + 30*alpha(3,6)*s3^4*(s3 - 1) - 15*...
         alpha(3,5)*s3^4*(2*s3 - 2) - 60*alpha(3,3)*s3^2*(s3 - 1)^3 + 60*alpha(3,4)*s3^2*(s3 - 1)^3 + 60*alpha(3,4)*...
         s3^3*(s3 - 1)^2 - 60*alpha(3,5)*s3^3*(s3 - 1)^2)/(2*deltheta);
  Dh_Dq(3,5)=0;
  Dh_Dq(4,1)=-(6*alpha(4,6)*s4^5 - 6*alpha(4,7)*s4^5 - 6*alpha(4,1)*(s4 - 1)^5 + 6*alpha(4,2)*...
         (s4 - 1)^5 + 30*alpha(4,2)*s4*(s4 - 1)^4 - 30*alpha(4,3)*s4*(s4 - 1)^4 + 30*alpha(4,6)*s4^4*(s4 - 1) - 15*...
         alpha(4,5)*s4^4*(2*s4 - 2) - 60*alpha(4,3)*s4^2*(s4 - 1)^3 + 60*alpha(4,4)*s4^2*(s4 - 1)^3 + 60*alpha(4,4)*...
         s4^3*(s4 - 1)^2 - 60*alpha(4,5)*s4^3*(s4 - 1)^2)/deltheta;
  Dh_Dq(4,2)=-(6*alpha(4,6)*s4^5 - 6*alpha(4,7)*s4^5 - 6*alpha(4,1)*(s4 - 1)^5 + 6*alpha(4,2)*...
         (s4 - 1)^5 + 30*alpha(4,2)*s4*(s4 - 1)^4 - 30*alpha(4,3)*s4*(s4 - 1)^4 + 30*alpha(4,6)*s4^4*(s4 - 1) - 15*...
         alpha(4,5)*s4^4*(2*s4 - 2) - 60*alpha(4,3)*s4^2*(s4 - 1)^3 + 60*alpha(4,4)*s4^2*(s4 - 1)^3 + 60*alpha(4,4)*...
         s4^3*(s4 - 1)^2 - 60*alpha(4,5)*s4^3*(s4 - 1)^2)/deltheta;
  Dh_Dq(4,3)=0;
  Dh_Dq(4,4)=-(6*alpha(4,6)*s4^5 - 6*alpha(4,7)*s4^5 - 6*alpha(4,1)*(s4 - 1)^5 + 6*alpha(4,2)*...
         (s4 - 1)^5 + 30*alpha(4,2)*s4*(s4 - 1)^4 - 30*alpha(4,3)*s4*(s4 - 1)^4 + 30*alpha(4,6)*s4^4*(s4 - 1) - 15*...
         alpha(4,5)*s4^4*(2*s4 - 2) - 60*alpha(4,3)*s4^2*(s4 - 1)^3 + 60*alpha(4,4)*s4^2*(s4 - 1)^3 + 60*alpha(4,4)*...
         s4^3*(s4 - 1)^2 - 60*alpha(4,5)*s4^3*(s4 - 1)^2)/(2*deltheta);
  Dh_Dq(4,5)=1;

end